Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias

Abstract

We study spherical collapse in the Quartic and Quintic Covariant Galileon\ngravity models within the framework of the excursion set formalism. We derive\nthe nonlinear spherically symmetric equations in the quasi-static and\nweak-field limits, focusing on model parameters that fit current CMB, SNIa and\nBAO data. We demonstrate that the equations of the Quintic model do not admit\nphysical solutions of the fifth force in high density regions, which prevents\nthe study of structure formation in this model. For the Quartic model, we show\nthat the effective gravitational strength deviates from unity at late times ($z\n\\lesssim 1$), becoming larger if the density is low, but smaller if the density\nis high. This shows that the Vainshtein mechanism at high densities is not\nenough to screen all of the modifications of gravity. This makes halos that\ncollapse at $z \\lesssim 1$ feel an overall weaker gravity, which suppresses\nhalo formation. However, the matter density in the Quartic model is higher than\nin standard $\\Lambda$CDM, which boosts structure formation and dominates over\nthe effect of the weaker gravity. In the Quartic model there is a significant\noverabundance of high-mass halos relative to $\\Lambda$CDM. Dark matter halos\nare also less biased than in $\\Lambda$CDM, with the difference increasing\nappreciably with halo mass. However, our results suggest that the bias may not\nbe small enough to fully reconcile the predicted matter power spectrum with LRG\nclustering data.\n